# Convexly independent subsets of Minkowski sums of convex polygons

## TL;DR

This paper demonstrates that for certain convex polygons, the largest convex subset within their Minkowski sum can grow proportionally to n log n, matching known upper bounds.

## Contribution

It establishes the existence of convex polygons with Minkowski sums whose largest convex subset reaches the theoretical maximum size, advancing understanding of Minkowski sum properties.

## Key findings

- Largest convex subset in Minkowski sum can be Θ(n log n)
- Matches the upper bound established by Tiwary
- Provides examples of polygons achieving this bound

## Abstract

We show that there exist convex $n$-gons $P$ and $Q$ such that the largest convex polygon in the Minkowski sum $P+Q$ has size $\Theta(n\log n)$. This matches an upper bound of Tiwary.